String theory and post-empiricism

18208_Peter_Woit_HD_Wallpaper_Pic.jpgby Peter Woit

Last month’s conference in Princeton included two remarkable talks by prominent physicists, both of whom invoked philosophy in a manner unprecedented for this kind of scientific gathering. On the first day, Paul Steinhardt attacked the current practice of inflationary cosmology as able to accommodate any experimental result, so, on philosophical grounds, no longer science [2]. He included a video clip of Richard Feynman characterizing this sort of thing as “cargo cult physics.” On the final day, David Gross interpreted Steinhardt’s talk as implicitly applying to string theory, then went on to invoke a philosopher’s new book to defend string theory, arguing that string theorists needed to read the book in order to learn how to defend what they do as science [3].

The book in question was Richard Dawid’s String Theory and the Scientific Method [4], which comes with blurbs from Gross and string theorist John Schwarz on the cover. Dawid is a physicist turned philosopher, and he makes the claim that string theory shows that conventional ideas about theory confirmation need to be revised to accommodate new scientific practice and the increasing significance of “non-empirical theory confirmation.” The issues of this kind raised by string theory are complex, so much so that I once decided to write a whole book on the topic [5]. A decade later I think the arguments of that book still hold up well, with its point of view about string theory now much more widespread among working physicists. One thing I wasn’t aware of back then was the literature in philosophy of science about “progressive” vs. “degenerating” research programs, which now seems to me quite relevant to the question of how to think about evaluating string theory.

I’ve written a bit about the Dawid book and earlier work of his [6], although as for any serious book there’s of course much more to say, even if I lack the time or energy for it. Recently an interview with Dawid appeared, entitled “String theory and post-empiricism,” which summarizes his views and makes some claims about string theory critics which deserve a response, so that will be the topic here. In the interview he says:

I think that those critics make two mistakes. First, they implicitly presume that there is an unchanging conception of theory confirmation that can serve as an eternal criterion for sound scientific reasoning. If this were the case, showing that a certain group violates that criterion would per se refute that group’s line of reasoning. But we have no god-given principles of theory confirmation. The principles we have are themselves a product of the scientific process. They vary from context to context and they change with time based on scientific progress. This means that, in order to criticize a strategy of theory assessment, it’s not enough to point out that the strategy doesn’t agree with a particular more traditional notion.

Second, the fundamental critics of string theory misunderstand the nature of the arguments which support the theory. Those arguments are neither arbitrarily chosen nor uncritical. And they are not decoupled from observation. String theory is indirectly based on the empirical data that drove the development of those theories string theory aims to unify. But more importantly for our discussion, the arguments for the viability of string theory are based on meta-level observations about the research process. As described before, one argument uses the observation that no-one has found a good alternative to string theory. Another one uses the observation that theories without alternatives tended to be viable in the past.

Taking the second part of this first, Dawid seems to be claiming that Smolin and I don’t understand what he calls the “No Alternatives Argument” (discussed in detail in his book, as well as in a paper in The British Journal for the Philosophy of Science [8]. In response I’ll point out that one of the concluding chapters of my book was entitled “The Only Game in Town” and was devoted explicitly to this argument. To this day I think that a version of such an argument is the strongest one for string theory, and is what motivates most physicists who continue to work on the theory. The version of this argument that I hear often privately and that has been made publicly by theorists like Edward Witten goes something like:

Ideas about physics that non-trivially extend our best theories (e.g. the Standard Model and general relativity) without hitting obvious inconsistency are rare and deserve a lot of attention. While string theory unification hasn’t worked out as hoped, we have learned a lot of interesting and unexpected things by thinking about string theory. If they see a new idea that looks more promising, string theorists will shift their attention to that.

This is a serious argument, one that I tried to carefully address in the book. Beyond that, more naive versions of it seem to me to have all sorts of obvious problems. Of course, if you really can show that alternatives to a given model are impossible, that is a convincing argument for the model, but this is rarely if ever possible. Working scientists beating their heads against a hard problem are always in the position of having “no alternatives” to some flawed ideas, until the day when someone solves the problem and finds the alternative. The only example I can recall seeing from Dawid of a successful example of the “no alternatives argument” is the discovery of the Higgs, and I find that very hard to take seriously. Pre-2012, the Standard Model was a very precise and exhaustively tested theory, providing a huge amount of indirect evidence for the Higgs. There were plenty of alternatives (technicolor, SUSY, etc.), all much more complicated and with no evidence for them. Making a “no alternatives argument” for a theory with overwhelming experimental evidence behind it is something completely different than trying to do the same thing for a theory with zero experimental evidence.

As for the other mistake that Dawid thinks string theory critics make, that of believing in some unchanging notion of empirical theory confirmation, the first thing to point out is that of course every theorist is well aware that one can can’t just demand experimental predictions and confirmation for ideas, that one spends basically all one’s time working on better understanding ideas that are far from the point where empirical confirmation comes into play. The second thing to point out is that I agree completely with Dawid that as experiments become more difficult, one needs to think about other ways of evaluating ideas to see if they are going anywhere. The last chapter of my book was devoted to exactly this question, arguing that physicists should look carefully at how mathematicians make progress. Mathematics is certainly “post-empirical,” and while logical rigor is a constraint, it is not one that necessarily points mathematicians to fertile new ideas. There is a long history and a deeply-ingrained culture that helps mathematicians figure out the difference between promising and empty speculation, and I believe this is something theoretical physicists could use to make progress.

The epigram from that last chapter though was something that kept going through my head when thinking about this, a line from Bob Dylan’s “Absolutely Sweet Marie”:

But to live outside the law, you must be honest.

Yes, theoretical particle physics is in a stage where empirical results are not there to keep people honest, and new and better “post-empirical” ways of evaluating progress are needed. But these must come with rigorous protections against all-too-human failings such as wishful thinking and Lee Smolin’s “groupthink,” and I just don’t see those anywhere in Dawid’s proposal for new kinds of theory confirmation.

_____

I’d like to thank Massimo Pigliucci for the opportunity to write something here at Scientia Salon, and hope it will generate an interesting discussion. Contributions from philosophers to this kind of debate in physics I believe are very much needed, on this issue and others. Don’t even get me started about the multiverse…

 

Peter Woit is an American theoretical physicist. He is a Senior Lecturer in the Mathematics department at Columbia University. Woit is especially known for his criticism of string theory in his book Not Even Wrong, and also for his widely-read blog of the same name. Peter was one of the first guests on the Rationally Speaking podcast.

[1] Strings 2014 conference.

[2] Paul Steinhardt’s presentation.

[3] David Gross’ presentation.

[4] String Theory and the Scientific Method, by Richard Dawid.

[5] Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law for Unity in Physical Law, by Peter Woit.

[6] Woit on Dawid: here and here.

[7] String theory and post-empiricism, interview with Richard Dawid.

[8] The No Alternatives Argument, by Richard Dawid.

156 thoughts on “String theory and post-empiricism

  1. To a certain extent, this issue is a bit like epicycles, in that since the math works, the physical theories must be right and so the hunt is on for the next great cosmic gearwheel/patch between theory and observation.
    Just as a supposition, what if there is no ‘fabric of spacetime’ and it is simply an elaborate correlation of measures of distance and duration? We could create a similar framework, using ideal gas laws to create ‘temperaturevolume.’
    We experience time as a sequence of events and physics distills this to measures of duration, but that is our individual perception of change. The point of the present isn’t moving from past to future, so much as change turns future into past. Tomorrow becomes yesterday because the earth turns. What we are measuring is frequency, just as with temperature, we are measuring cumulative amplitude. Time is an effect of action, like temperature. That is why there is no universal measure of time, just the cumulative effect of lots of actions.
    In fact, a faster clock ‘ages/burns’ more rapidly, so it recedes into the past quicker.
    As this removes time from that ‘fabric,’ it leaves space without a frame, absolute and infinite.
    Not a popular notion, but maybe worth considering.

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  2. Hi Coel,

    I still maintain that maths is ultimately empirical, with axioms of maths being derived from reality as a distillation of empiricism.

    Are there maths axioms that are not? Well, the Axiom of Choice perhaps, but then that produces Banach–Tarski which more or less proves my point. Anyone who accepts Banach–Tarski certainly has gone over to the Dark Side!

    I think that this more or less shows the problem with your position.

    What is there not to accept about Banach-Tarksi? Have they made some technical error in their proofs?

    As far as I know they have not.

    Is there some stone tablet that says you should not use the axiom of choice and I have not got the memo?

    I don’t think so.

    So it is not so much that you think that maths is ultimately empirical, it is just that you don’t like the maths that is not empirically based.

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  3. Does anyone here think that modern philosophers have contributed something useful to this topic? String theory has failed to make a testable prediction, or to reproduce existing theory. The Standard Model has succeeded in LHC experiments. Thus the Standard Model has won. Modern philosophy of science has contributed nothing.

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  4. The 2014 string conference showed that string theorists have given up on the aim to provide a framework of unification. As such, string theory is not the only game in town. First of all, they are not playing any more.

    Secondly there are other games in town that have not given up playing. These other games still check their results with data. For example, one game avoids all of Peter Woits’s criticism, and on top approximates the Higgs mass and the fine structure constant. It is found at http://www.motionmountain.net/research.html

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  5. Thanks Christopher, for that scientific assessment of Larson’s theory. Unfortunately, it doesn’t invalidate the philosophical objection against the atomic hypothesis (the claim that all matter is ontologically reducible to atomic particles). The philosophical case against the atomic thesis is immune to objections based on induction from empirical data, thanks to the observer effect (the fact that atomic theory cannot account for the role of the human cognitive faculties in structuring the observed data, since the same faculties are necessarily relied upon in any attempt to account for such a role).

    So the fact that atomic theory makes accurate predictions doesn’t invalidate the philosophical argument that atoms do not exist in the absence of consciousness, and are indeed an aspect of consciouness. I think the philosophical case has merit, because there appear to be good reasons for doubting that causation exists in the absence of consciousness. Rather than being mind-independent, ‘causation’ appears to be a heuristic notion that consciousness uses to structure experience. This conclusion runs counter to the atomic hypothesis, in which atoms are posited to be mind-independent entities that are causally and therefore logically prior to conscious experience. I outline the philosophical objection in my article at http://philsci-archive.pitt.edu/10714/

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  6. Epicycles had the virtue of theory matching observation. String theory has not achieved that.

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  7. Hi Robin,

    … it is just that you don’t like the maths that is not empirically based.

    Exactly, I don’t like maths that is nonsensical in real-world terms (I await someone demonstrating Banach–Tarski with a potato and carving knife, and coincidentally ensuring that no-one ever again goes hungry).

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  8. That is an exceedingly narrow conception of math, and I’m pretty sure you’ll find few if any mathematicians that endorse it. (Of course, that truly is an empirical question…)

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  9. There are actually very few things in maths that are “nonsensical” in comparison with the real world, meaning that they are in direct contradiction to it (Banach–Tarski being noted and discussed as a rare example of that).

    There is plenty of maths that might not be directly empirically relevant, but is still entirely consistent with the real world (being, as I assert, built on axioms that derive from the real world).

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  10. Rolls eyes, sighs despairingly.

    Thus the Standard Model has won
    Has won what?
    Was there war?
    Was there a race? (who was racing?)

    Modern philosophy of science has contributed nothing
    What do you think it should have contributed?
    Do you know what philosophy is?

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  11. I have no idea what you mean by “entirely consistent with the real world.” Consider, for instance, the math that describes a particular type of multidimensional space, folded in a particular way. Suppose also that it turns out that real space has a different number of dimensions, folded in a different way. In what sense could the math then be said to be “consistent” with the real world, since it describes a world that doesn’t exist? And let’s not get started on possible worlds logic…

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  12. Hi Massimo,

    Consider, for instance, the math that describes a particular type of multidimensional space, folded in a particular way.

    Not that I endorse Coel’s view, but it seems to me that this is just the math that describes real space applied to a slightly different setup. It’s derived from the real world but manipulated in ways consistent with human imagination, which is also derived from the real world. This is not so unlike any act of human creation. A new design for a widget is, before it’s manufactured at least, describing something that does not exist, but the design is based on extrapolating from real-world knowledge.

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  13. DM, no, sorry, it just isn’t, and to claim so is to stretch “compatible with the real world” beyond any sensible meaning.

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  14. Hi Coel,

    Exactly, I don’t like maths that is nonsensical in real-world terms

    This is probably your one and only area of agreement with Bishop George Berkeley.

    I always thought it odd that Berkeley didn’t like maths that didn’t apply to the real world when he didn’t believe in a real word.

    (I await someone demonstrating Banach–Tarski with a potato and carving knife, and coincidentally ensuring that no-one ever again goes hungry).

    But that is the thing about maths. It doesn’t need to be empirically proven.

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  15. Yes, there is a competition to find the best theories for high-energy physics. Many leading physicists were openly hoping that the LHC would falsify the Standard Model so that competing theories could gain traction.

    I do think that philosophy of science should be able to say something about whether string theory is a worthwhile scientific endeavor.

    I read Pigliucci’s complaint that Tyson said that “philosophy has basically parted ways from the frontier of the physical sciences” in the early 20th century. Sorry, but Tyson is right. It is nearly impossible to find any philosopher who has anything worthwhile to say about 20th century physics. Dawid’s post-empiricism is just the latest example of foolishness, as Woit explains.

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  16. Hi Massimo,

    I have no idea what you mean by “entirely consistent with the real world.”

    I mean that there is no contradiction. Mathematics is about patterns, and the concept of n-dimensional space is very general. For example I can talk about a “chi-squared landscape in n-dimensional parameter space”. There is no contradiction in making statements about that n-dimensional parameter space, and at the same time making statements about a different-dimensional space.

    Of course there would be a contradiction if I asserted both that “physical space is n-dimensional” and “physical space is n+1-dimensional”, but there is no contradiction if I say that “physical space is n-dimensional” and “such and such a pattern holds in n+1-dimensional space”.

    The problem with Banach-Tarski is that it does directly contradict the patterns that hold in the real world.

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  17. Unfortunately I don’t accept your distinction. In particular science deals with “concepts” as much as anything does, and concepts are unavoidably entwined with empiricism (Duhem–Quine).

    If you like we could make a distinction between concepts that have some relation and relevance to the real world and concepts that don’t, but that distinction doesn’t map neatly to the areas you list.

    When you invoke Quine in support of your position, don’t forget that Quine is not using “empiricism” in the same sense you are using it.

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  18. There are actually very few things in maths that are “nonsensical” in comparison with the real world, meaning that they are in direct contradiction to it (Banach–Tarski being noted and discussed as a rare example of that).

    There is plenty of maths that might not be directly empirically relevant, but is still entirely consistent with the real world (being, as I assert, built on axioms that derive from the real world).

    Naturally, because the real world behaves mathematically.

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  19. I read Pigliucci’s complaint that Tyson said that “philosophy has basically parted ways from the frontier of the physical sciences” in the early 20th century. Sorry, but Tyson is right. It is nearly impossible to find any philosopher who has anything worthwhile to say about 20th century physics.

    On the contrary, the early 20th century was when physics went into a mind meld with philosophy.

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  20. Hi Robin,

    Naturally, because the real world behaves mathematically.

    Yes, we’re agreed on this.

    But, does the real world behave as described by Banach–Tarski?

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  21. The world does indeed behave in a way that is consistent with mathematical descriptions of 12-dimensional and 25-dimensional space (meaning, there is no contradiction between statements about how the world works and statements about patterns in those n-dimensional spaces).

    That’s different from Banach–Tarski which is in contradiction to real-world behaviour. Either 3-dimensional solid objects behave as in the real world or they behave as in Banach–Tarski, but not both.

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  22. My point is that String Theory is an effort to patch General Relativity and Quantum Mechanics, both of which are very mathematically accurate, like epicycles, but the physical explanations of which have problems matching our observations of reality.
    So could there be assumptions built into the foundations of these theories which are causing problems? Such as time being treated as a measurement and then this as a fundamental mathematical factor. The issues of blocktime and symmetry of time seem as physically problematic as multiworlds, dark matter, dark energy, inflation, multiverses, etc.
    If we consider time to be an effect of action, such that future becomes past, then there is no need for blocktime and time is asymmetric because of inertia. Action doesn’t stop and go the other direction, since the energy required would be a factor in itself.
    Also it would explain why the future is probabilistic and the past is deterministic. Since the speed information travels is finite, the input into any event only arrives with its occurrence. So no need to assume the future must be determined, or the past remains probabilitic, ie. branching out into multiworlds. There are ten potential winners before a race and one actual winner after it.
    As for cosmology, how can it even be argued space expands, but then the galaxies recede, since this would assume a constant speed of light across that expanding distance. If the speed of light is being used as a denominator, then the expansion is a numerator and that would be increasing distance, not expanding space.

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  23. Which completely misses my point: if math is supposed to describe reality, the latter either has12 or 25 dimensions, not both, and probably neither.

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  24. No contradiction btw a description based on 12 vs one based on 25 dimensions?

    A mathematical description of 12-dimensional space is not *about* physical space, it is about 12-dimensional space. It is thus consistent with (= doesn’t contradict) descriptions of physical space.

    In the same way “John is tall” is about John, not about Alex, so is consistent with “Alex is short”.

    Saying “physical space is both 12-dimensional and 25-dimensional” would be inconsistent. But merely making statements about both 12-D space and 25-D space is not inconsistent.

    The point about Banach-Tarski is that it is about solid, 3-dimensional objects of the sort that we kick when we play football, and it makes statements about them that are inconsistent with (= contradict) real-world behaviour of those same objects. Thus we have a contradiction of the form “John is tall” and simultaneously “John is short”.

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  25. Which completely misses my point: if math is supposed to describe reality, the latter either has12 or 25 dimensions, not both, and probably neither.

    The physical space that we inhabit is only one aspect of reality. For example, if I have a 12-parameter model then I have a “chi-squared landscape” inhabiting a 12-dimensional parameter space. Ditto for a 25-parameter model. These are entirely valid concepts about reality, in that they describe the real-world behaviour of that model.

    But anyhow, I have no problem with maths that is consistent with the real world, even if not necessarily implemented in the real world — in that sense maths is just considering implications of axioms, even though those implications may not be actually extant as physical entities.

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  26. Which completely misses my point: if math is supposed to describe reality, the latter either has12 or 25 dimensions, not both, and probably neither.

    If it misses the point, then your point misses Coel’s.

    Empirically, we can figure out how geometry works in 3 dimensions. It’s relatively straightforward to extend this to other numbers of dimensions. It’s a simple extrapolation, but ultimately rooted in what we can see around us. A mathematical structure describing 12- or 25- dimensional space does not contradict reality. It exists in addition to and alongside mathematical structures which describe reality, just as triangles exist alongside squares.

    So the difference between you is that Coel thinks mathematics is derived from reality as long as its development can be traced in terms of extrapolations from reality. You seem to think that mathematics can only be derived from reality if it is directly relatable to what we see around us.

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  27. Hi Coel,

    That’s different from Banach–Tarski which is in contradiction to real-world behaviour. Either 3-dimensional solid objects behave as in the real world or they behave as in Banach–Tarski, but not both.

    Actually, I’m not convinced that Banach-Tarski does not contradict the real world. The problem is that it is interpreted incorrectly.

    Banach Tarski is not about carving up a physical solid object. It’s about carving up an infinitely divisible volume consisting of an infinite number of points. Paradoxes not too dissimilar from Banach Tarski in their conclusions are familiar from fields such as fractal geometry, where different ways of measuring the length or volume of a shape can give different results.

    A physical ball is made of atoms. It is not a fractal structure, infinitely divisible. The ball itself doesn’t contain an infinite number of points even if the actual volume it occupies does (if space is not quantized). The ball itself really only contains points as defined by the atoms or molecules it is made of. These cannot be divided, so Banach Tarski does not apply.

    The idea that we can divide up an empty volume of space and move the divisions around so as to create two volumes of empty space does not seem to me to be all that strange. 0 = 0 + 0

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  28. I would be interested to hear how string theory is going to solve any of those supposed problems.

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  29. Let me clarify that; String Theory is a failed effort to patch General Relativity and Quantum Mechanics,

    What I listed were not the problems, but the proffered solutions to problems. As String Theory was a proffered(unsuccessful) solution to the problem of uniting GR and QM.

    There is nothing wrong with speculative projection, but physics seems to be carrying this to extremes and not recognizing it as such. For example, when accountants get too inventive with the math, it can attract unwanted legal attention, but physical theorists seem to think every passing notion must be a window into another universe.

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  30. woit: “… Yes, experiment trumps others, but there really are worthwhile theory selection criteria other than agreement with experiment.”

    Amen! But, can you elaborate this more. I have proposed a ‘beauty-contest’ criterion on this ‘post-empirical theory confirmation’ issue, with the following steps.

    1. Establish anchors: the solidly accepted physics {such as: uncertainty principle, light speed, ħ, Alpha (fine structure constant), Planck data (dark energy = 69.2; dark matter = 25.8; and visible matter = 4.82), Weinberg angle, Standard Model particles (string unification), etc.}.
    2. The competing theories are competing on matching with those anchors. First by numbers (how many matched), second by parsimony (by number of axioms or hypotheses needed in the theory). See, http://putnamphil.blogspot.com/2014/06/a-final-post-for-now-on-whether-quine.html?showComment=1403329115355#c4963720466770510827 .

    In fact, instead of ‘discovering’ laws of nature, we can actually ‘design’ a universe and deduce (derive) the laws of this designed-universe. Then, a beauty-contest can be set up between the ‘discovered-laws’ and ‘the derived-laws’.

    Thanks for the link to the Paul Steinhardt’s presentation which is now advocating the “bounce (from big crunch to big bang)”. This cyclic universes was briefly discussed at this Webzine (Scientia Salon), see https://scientiasalon.wordpress.com/2014/06/05/the-multiverse-as-a-scientific-concept-part-ii/comment-page-1/#comment-3158 . That is, the ‘bounce’ is not a new idea of Steinhardt. Looking forward to your comment on this too.

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  31. Hi DM,

    The idea that we can divide up an empty volume of space and move the divisions around so as to create two volumes of empty space does not seem to me to be all that strange.

    Doesn’t it? So are you intuitively happy about the idea of creating more volume just by rotating it?

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  32. So are you intuitively happy about the idea of creating more volume just by rotating it?

    I wouldn’t say I’m intuitively happy with it. I would say I wouldn’t presume that my intuition can tell me anything useful about what volume means for inflinitely complex fractal structures.

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  33. As I understand it, Banach Tarski starts with entirely normal intuitive volume that supposedly corresponds to the normal volume of physical space.

    Then B-T does some hocus-pocus by dividing it up infinitely into weird unmeasurable sets, and then starts dividing those unmeasurable sets up further, and selects from those sets using the axiom of choice, and then proceeds to add up those weird infinite sets again into normal, sensible volumes.

    And as a result of that B-T declares that by simply rotating an entirely normal volume you can create more volume. The starting and end points are things about which intuition should be pretty reliable, yet the result is counterintuitive (to put it mildly). You can excuse me for being somewhat dubious about that process and for suspecting that there is something very fishy about these infinite unmeasurable sets.

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  34. “… ideas about physics that non-trivially extend our best theories (e.g. the Standard Model and general relativity) without hitting obvious inconsistency are rare and deserve a lot of attention.”

    It’s weird that Dr Peter Woit claims that this “there is no alternative so you must believe in M-theory” argument is difficult to respond to, seeing that he debunked it in his own 2002 arXiv paper “Quantum field theory and representation theory”.

    In that paper he makes the specific point about the neglect of alternatives due to M-theory hype, by arguing there that a good alternative is to find a symmetry group in low dimensions that encompasses and explains better the existing features of the Standard Model.

    Woit gives a specific example, showing how to use Clifford algebra to build a representation of a symmetry group that for 4 dimensional spacetime predicts the electroweak charges including left handed chiral weak interactions, which the Standard Model merely postulates.

    But he also expresses admiration for Witten, whose first job was in left wing politics, working for George McGovern, a Democratic presidential nominee in 1972. In politics you brainwash yourself that your goal is a noble one, some idealistic utopia, then you lie to gain followers by promising the earth. I don’t see much difference with M-theory, where a circular argument emerges in which you must

    (1) shut down alternative theories as taboo, simply because they haven’t (yet) been as well developed or hyped as string theory, and

    (2) use the fact that you have effectively censored alternatives out as being somehow proof that there are “no alternatives”.

    I don’t think Dr Woit is making the facts crystal clear, and he fails badly to make his own theory crystal clear in his 2002 paper where he takes the opposite approach to Witten’s hype of M-theory. Woit introduces his theory on page 51 of his paper, after a very abstruse 50 pages of advanced mathematics on group symmetry representations using Lie and Clifford algebras. The problem is that alternative ideas that address the core problems are highly mathematical and need a huge amount of careful attention and development. I believe in censorship for objectivity in physics, instead of censorship to support fashion.

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  35. and then proceeds to add up those weird infinite sets again into normal, sensible volumes.

    No, not really. The volumes so created are anything but normal or sensible. As I understand it they are fractally complex and interleaved in funny ways not possible with ordinary matter.

    So if the paradox is weird, it is not hugely weirder to me than that the coastline of Britain is potentially infinitely long (http://en.wikipedia.org/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension).

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  36. The Milgrom-McGaugh-Kroupa-Pawlowski line of evidence rules out the ΛCDM model. There exists another line of evidence that rules out the ΛCDM model.
    “… either conventional sources of ionizing photons (galaxies and quasars) must contribute considerably more than current observational estimates or our theoretical understanding of the low-redshift universe is in need of substantial revision.”
    http://iopscience.iop.org/2041-8205/789/2/L32/article “The Photon Underproduction Crisis”
    http://arxiv.org/abs/1404.2933 “The Photon Underproduction Crisis”, 10 Apr 2014′
    My guess is that string theorists have attacked the wrong target: They think that Heisenberg’s uncertainty principle should be replaced by a new uncertainty principle involving both hbar and alpha-prime. I think that Einstein’s equivalence principle should be replaced and the Heisenberg uncertainty principle should not be replaced.

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  37. Hi Coel,

    Yes, we’re agreed on this.

    But, does the real world behave as described by Banach–Tarski?

    No, and that is the point. Maths describes the way the real world works but it is not limited to describing how the real world works. And why should it, apart from your arbitrary prejudice about the matter.

    And in fact, according to you and DM it is only pot luck that reality is such that Banach-Tarski objects are not instantiable as actuals (since they are entirely logically consistent). If reality had been such that Banach-Tarski objects were instantiable then your counterpart in that world would be complaining that people who didn’t accept the Axiom of Choice were on the dark side.

    So, according to your metaphysical position Banach-Tarski objects represent types of reality that, for no reason at all, don’t happen to be the case.

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  38. The volumes so created are anything but normal or sensible.

    Surely the whole point is that the volume you start with (before infinite decomposition) and the volume you end with (after reconstruction) are indeed normal and sensible volumes. That’s why it is paradoxical. If it were only about infinite fractal spaces then that would be rather different.

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  39. I would like to add these conceptual shortcuts go much deeper than spacetime. Mathematicians have no problem with dimensionless points, lines, dimensions, etc, yet even in the abstract, anything multiplied by zero is zero. A dimensionless point is no more real than a dimensionless apple. Yet it is much easier than trying to qualify it with some infinitesimal dimensionality. Keep in mind though, that if an accountant were to try this sort of thing, it would fall very much in the category of fraud, yet the assumption seems to be these invisible abstractions are some platonic basis of reality.
    Zero means zero.

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  40. The abstract to Dawid’s “No Altenatives” paper reads as follows: “Scientific theories are hard to find, and once scientists have found a theory, H, they often believe that there are not many distinct alternatives to H. But is this belief justified? What should scientists believe about the number of alternatives to H, and how should they change these beliefs in the light of new evidence? These are some of the questions that we will address in this article. We also ask under which conditions failure to find an alternative to H confirms the theory in question. This kind of reasoning (which we call the ‘no alternatives argument’) is frequently used in science and therefore deserves a careful philosophical analysis”.

    First, “is frequently used in science”: where else is it used, apart from by string theorists?

    Second, the underlying metaphysical assumption is that a certain kind of theoretical unification of all forces exists. But there may be no such theory. Indeed as Einstein showed, gravity is *not* a force, it is a manifestation of spacetime curvature. It is therefore rather unlikely that any such unified theory exists that includes gravity.The whole thing hinges on that a priori metaphysical assumption – which may well be false.

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  41. “But there may be no such theory. Indeed as Einstein showed, gravity is *not* a force, it is a manifestation of spacetime curvature.”

    This is a pretty good example of a “no alternatives” delusion: if gravity is quantized in quantum field theory, the gravitational force will then be mediated by graviton exchange (gauge bosons), just like any Standard Model force, not spacetime curvature as it is in general relativity. Note that Einstein used rank-2 tensors for spacetime curvature to model gravitational fields because that Ricci tensor calculus was freshly minted and available in the early 20th century.

    Rank-2 tensors hadn’t been developed to that stage at the time of Maxwell’s formulation of electrodynamics laws, which uses rank-1 tensors or ordinary vector calculus to model fields as bending or diverging “lines” in space. Lines in space are rank 1, spacetime distortion is rank 2. The vector potential version of Maxwell’s equations doesn’t replace field lines with spacetime curvature for electromagnetic fields, it merely generalizes the rank-1 field description of Maxwell. It’s taboo to point out that electrodynamics and general relativity arbitrarily and dogmatically use different mathematical descriptions for reasons of historical fluke, not physical utility (rank 1 equations for field lines versus rank 2 equations for spacetime curvature). Maxwell worked in a pre-tensor era, Einstein in a post-tensor era. Nobody bothered to try to replace Maxwell’s field line description of electrodynamics with a spacetime curvature description, or vice-versa to express gravitational fields in terms of field lines. It’s taboo to even suggest thinking about it! Sure there will be difficulties in doing so, but you learn about physical reality by overcoming difficulties, not by making it taboo to think about.

    The standard dogma is to assert that somehow just because Maxwell’s model is rank 1 and involves spin 1 gauge boson exchange when quantized as QED, general relativity involves a different spin to couple to the rank 2 tensor, spin 2 gravitons. However, since 1998 it’s been observationally clear that the cosmological acceleration implies a repulsive long range force between masses, akin to spin-1 boson exchange between similar charges (mass-energy being the gravitational charge). If you take this cosmological acceleration or repulsive interaction or “dark energy” as the fundamental interaction, you can obtain general relativity’s “gravity” force (attraction) in the way the Casimir force emerges.

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